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Lorentzian geometry is a vivid field of mathematical research that can be seen as part of differential geometry as well as mathematical physics. It represents the mathematical foundation of the general theory of relativity - which is probably one of the most successful and beautiful theories of physics.
In this project, we fuel our research with ideas from theoretical physics. For example, properties of Lorentzian manifolds like causality are linked with properties of a so-called observer field that represents the velocity field of the matter content in the respective spacetime. Geometrically, this observer field represents a time orientation, and the irreducible parts of its covariant derivative can be physically interpreted as rotation, shear and expansion of the spacetime model.
These quantities are called kinematical invariants and play a prominent role in the construction of cosmological models, thermodynamics in curved spacetime and so on. We believe that the kinematical invariants also play an important role in the study of Lorentzian geometry in its own right.